If you think that's only public school you're deluding yourself. My secondary education was in private schools (in the US sense of the word) and I have no issue whatsoever seeing this scenario unroll there (I can even cast the parts).
Petty tyrants is what you get when petty people get access to any sort of power to lord over others, the exact nature of that power has little relevance. The concentration of petty tyrants is only a function of how easy it is to be granted power by the environment.